In a large bowl, combine ground turkey, oregano, garlic powder, and black pepper. Mix until well incorporated.
Add a drizzle of olive oil to a large skillet over medium heat.
Lay a corn tortilla flat and scoop about 2 tablespoons of turkey mixture onto one side. Press it evenly to form a thin layer.
Place the tortilla in the hot skillet, meat-side down. Cook until the turkey is browned and cooked through (internal temp of 165°F), about 3–4 minutes per side. Flip carefully to crisp the tortilla on both sides.
Spoon 1 tablespoon of tomato sauce over the cooked turkey side, then sprinkle with mozzarella and Parmesan.
Cover the skillet with a lid and cook another minute or two, until the cheese is melted and gooey.
Remove tacos from the pan, sprinkle with fresh basil, and serve hot.